Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x \left (a+b \text{csch}\left (c+d x^2\right )\right )},x\right ) \]
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Rubi [A] time = 0.027688, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{x \left (a+b \text{csch}\left (c+d x^2\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x \left (a+b \text{csch}\left (c+d x^2\right )\right )} \, dx &=\int \frac{1}{x \left (a+b \text{csch}\left (c+d x^2\right )\right )} \, dx\\ \end{align*}
Mathematica [A] time = 5.00693, size = 0, normalized size = 0. \[ \int \frac{1}{x \left (a+b \text{csch}\left (c+d x^2\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.061, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ( a+b{\rm csch} \left (d{x}^{2}+c\right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -2 \, b \int \frac{e^{\left (d x^{2} + c\right )}}{a^{2} x e^{\left (2 \, d x^{2} + 2 \, c\right )} + 2 \, a b x e^{\left (d x^{2} + c\right )} - a^{2} x}\,{d x} + \frac{\log \left (x\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{b x \operatorname{csch}\left (d x^{2} + c\right ) + a x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \left (a + b \operatorname{csch}{\left (c + d x^{2} \right )}\right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b \operatorname{csch}\left (d x^{2} + c\right ) + a\right )} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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